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一、基本概念
1、天体的真高度：地平坐标系中的一个坐标。从测者真地平圈起沿天体方位圈度量到天体中心的大圆弧距。
数值由0°至90°，向上度量为正，向下度量为负
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一、基本概念
1、天体的真高度：地平坐标系中的一个坐标。从测者真地平圈起沿天体方位圈度量到天体中心的大圆弧距。
数值由0°至90°，向上度量为正，向下度量为负
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一、基本概念
1、天体的真高度：地平坐标系中的一个坐标。从测者真地平圈起沿天体方位圈度量到天体中心的大圆弧距。
数值由0°至90°，向上度量为正，向下度量为负
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                                <h2>
                                    3.10 纯几何天文定位方法
                                </h2>
                                <span class="article-info">
                                    2023-11-25, 2975 words, 11 min read
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                            <div class="post_content markdown">
                                <p class="md_block">
                                    <span class="md_line md_line_start md_line_end">
                                        <p>星图模拟：给定任意姿态</p>
<p>星光定姿：实拍星图   姿态</p>
<p>星图匹配：三角形 栅格</p>
<h2 id="一-基本概念">一、基本概念</h2>
<p>1、天体的真高度：<strong>地平坐标系</strong>中的一个坐标。从测者真地平圈起沿天体方位圈度量到天体中心的大圆弧距。</p>
<p>数值由0°至90°，向上度量为正，向下度量为负</p>
<p>2、测量天体高度的精密测角仪器：航海六分仪</p>
<p>3、天文钟可以读取准确的世界时，作为航海天文历的引数查取天体坐标。</p>
<p>4、天体投影点 <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>G</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">GP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault">G</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span></span></span></span>： 天体与地心连线与地球表面的交点。</p>
<p>5、等高圆： 以天体投影点GP为圆心，天顶距Z为半径（天顶距<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>Z</mi></mrow><annotation encoding="application/x-tex">Z</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">Z</span></span></span></span>+天体高度<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault">h</span></span></span></span>=90°）</p>
<img src="http://cos.pansis.site/202311222127064.png/abc123" alt="image-20231122212752972" style="zoom:33%;" />
<p>这个圆叫做天文船位圆，圆心和半径各是天体地理位置,天体真顶距</p>
<h2 id="二-传统航海天文定位原理">二、传统航海天文定位原理</h2>
<h4 id="1-舰船天文导航的基本原理">1、舰船天文导航的基本原理</h4>
<p>1、利用六分仪测定两个已知天体的天体高度<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault">h</span></span></span></span>，利用修正公式进行修正，再计算其天顶距<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>Z</mi><mo>=</mo><mn>90</mn><mi mathvariant="normal">°</mi><mo>−</mo><mi>h</mi></mrow><annotation encoding="application/x-tex">Z=90°-h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">Z</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="mord">9</span><span class="mord">0</span><span class="mord">°</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault">h</span></span></span></span></p>
<p>2、查阅星历获取两个天体的位置，绘制两个等高圆。</p>
<p>3、船舶位置即在两个等高圆两个交点的其中一点。</p>
<h4 id="2-六分仪测角原理">2、六分仪测角原理</h4>
<img src="http://cos.pansis.site/202311222110387.png/abc123" alt="image-20231122211054155" style="zoom:40%;" />
<p>将六分仪目镜中的天体与水天线相重合。</p>
<p>所求量：<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault">h</span></span></span></span> 天体高度</p>
<p>已知量：<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>w</mi></mrow><annotation encoding="application/x-tex">w</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02691em;">w</span></span></span></span> 定镜与动镜的夹角</p>
<ul>
<li>当星体位于水天线时，指标镜和固定镜平行，BD//AC，这时，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>w</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">w=0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02691em;">w</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span></span></span></span>，天体高度<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>h</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">h=0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault">h</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span></span></span></span>。</li>
<li>当星体高于水天线时，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mi>β</mi><mo>=</mo><mi>h</mi><mo>+</mo><mn>2</mn><mi>α</mi></mrow><annotation encoding="application/x-tex">2\beta=h+2\alpha</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.05278em;">β</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="mord mathdefault">h</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.0037em;">α</span></span></span></span>  <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>β</mi><mo>=</mo><mi>α</mi><mo>+</mo><mi>w</mi></mrow><annotation encoding="application/x-tex">\beta=\alpha+w</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.05278em;">β</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathdefault" style="margin-right:0.0037em;">α</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02691em;">w</span></span></span></span> ，两式联立，消掉<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>β</mi></mrow><annotation encoding="application/x-tex">\beta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.05278em;">β</span></span></span></span>得<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>h</mi><mo>=</mo><mn>2</mn><mi>w</mi></mrow><annotation encoding="application/x-tex">h=2w</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault">h</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.02691em;">w</span></span></span></span></li>
</ul>
<p>调整指标杆使天体的像与地平线重合时，天体高度<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault">h</span></span></span></span>等于固定镜与指标镜夹角<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>w</mi></mrow><annotation encoding="application/x-tex">w</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02691em;">w</span></span></span></span>的二倍。</p>
<h4 id="3-六分仪特点">3、六分仪特点</h4>
<p>1、六分仪精度较低：机械误差不易控制，观测者的经验和习惯不同。受天气的影响大，不能在阴雨天使用，且风浪振动、摇摆及船上热空气流都有影响。</p>
<p>2、现代化舰船仍配有六分仪以备不时之需。</p>
<h4 id="4-六分仪的测量误差">4、六分仪的测量误差</h4>
<p>1、内容：标定误差、地平俯角误差、蒙气差、视差、视半径，</p>
<ul>
<li>
<p>地平俯角修正</p>
<ol>
<li>
<p>几大地平：测者地平、地面真地平、天文地平、视地平、地理地平</p>
<p>视地平：由于大气折射，测者视距由S点增远到F，F点光线沿曲线FA进入测者眼睛，在A点处切线AM称为视地平方向。</p>
<img src="http://cos.pansis.site/202311222128041.png/abc123" alt="image-20231122212852975" style="zoom:53%;" />
</li>
<li>
<p>地平俯角（Dip）： 测者地平相对于视地平的高度。（单位是角度）</p>
<p>公式：</p>
<img src="http://cos.pansis.site/202311222131162.png/abc123" alt="image-20231122213103103" style="zoom:50%;" />
</li>
<li>
<p>地平俯角修正公式：<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>2</mn></msub><mo>=</mo><msub><mi>H</mi><mn>1</mn></msub><mo>−</mo><mi>D</mi><mi>i</mi><mi>p</mi></mrow><annotation encoding="application/x-tex">H_2=H_1-Dip</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mord mathdefault">i</span><span class="mord mathdefault">p</span></span></span></span></p>
</li>
<li>
<p>高度<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">H_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>称为视高度，参考地平基准从视地平变成测者地平</p>
</li>
<li>
<p>当使用人工地平时，基准就是测者地平，Dip=0，无需地平俯角修正</p>
</li>
</ol>
</li>
<li>
<p>蒙气差修正</p>
<img src="http://cos.pansis.site/202311222131980.png/abc123" alt="image-20231122213148911" style="zoom:33%;" />
<ol>
<li>蒙气差R：由于大气折射（使光线向地心方向弯曲），观测者所见天体的视方向，是右图中曲线未端的切线AB的方向。它比真方向AB抬高的角度，就是蒙气差R。</li>
<li>蒙气差修正公式：<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>3</mn></msub><mo>=</mo><msub><mi>H</mi><mn>2</mn></msub><mo>−</mo><mi>R</mi></mrow><annotation encoding="application/x-tex">H_3=H_2-R</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span></span></span></span></li>
</ol>
</li>
<li>
<p>视差修正</p>
<img src="http://cos.pansis.site/202311222132509.png/abc123" alt="image-20231122213200995" style="zoom:33%;" />
<ol>
<li>修正的目的：将参考地平基准从测者地平变成天文地平</li>
<li>视差修正公式：<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>4</mn></msub><mo>=</mo><mi>P</mi><mo>+</mo><msub><mi>H</mi><mn>3</mn></msub></mrow><annotation encoding="application/x-tex">H_4=P+H_3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li>
<li>水平视差HP：天文地平（真地平）上天体的视差称为水平视差HP，可在天文年历中查到</li>
<li>视差P计算公式：<img src="http://cos.pansis.site/202311222132822.png/abc123" alt="image-20231122213226749" loading="lazy">  在右侧三角形内的正弦公式</li>
<li>需要改正视差的天体：月亮、金星、火星、太阳（视差依次减小，与距离有关系）</li>
</ol>
</li>
<li>
<p>视半径 (SD) 修正</p>
<ol>
<li>
<p>视半径:天体半径对于地心的最大张角。又称为半径差</p>
<img src="http://cos.pansis.site/202311222133166.png/abc123" alt="image-20231122213350108" style="zoom:33%;" />
</li>
<li>
<p>只有太阳和月亮考虑视半径。由于地球绕太阳公转和月亮绕地球公转的轨道都是椭圆，视半径会随时间的变化而变化，具体可查阅航海天文历。</p>
</li>
<li>
<p>修正公式：<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>5</mn></msub><mo>=</mo><msub><mi>H</mi><mn>4</mn></msub><mo>±</mo><mi>S</mi><mi>D</mi></mrow><annotation encoding="application/x-tex">H_5=H_4\pm SD</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span></span></span></span></p>
</li>
<li>
<p>月亮水平视差HP和视半径SD之间的关系（重点）</p>
</li>
<li>
<p><img src="http://cos.pansis.site/202311222135636.png/abc123" alt="image-20231122213559596" style="zoom:50%;" /><img src="http://cos.pansis.site/202311222135660.png/abc123" alt="image-20231122213531610" style="zoom:53%;" /></p>
</li>
</ol>
</li>
</ul>
<p>2、修正公式总结</p>
<ul>
<li>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>1</mn></msub><mo>=</mo><msub><mi>H</mi><mi>s</mi></msub><mo>−</mo><mi>I</mi><mi>E</mi></mrow><annotation encoding="application/x-tex">H_1=H_s-IE</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">I</span><span class="mord mathdefault" style="margin-right:0.05764em;">E</span></span></span></span>                   <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mi>s</mi></msub></mrow><annotation encoding="application/x-tex">H_s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>仪器实测读数  <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>I</mi><mi>E</mi></mrow><annotation encoding="application/x-tex">IE</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">I</span><span class="mord mathdefault" style="margin-right:0.05764em;">E</span></span></span></span> 标度误差</p>
</li>
<li>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>2</mn></msub><mo>=</mo><msub><mi>H</mi><mn>1</mn></msub><mo>−</mo><mi>D</mi><mi>i</mi><mi>p</mi></mrow><annotation encoding="application/x-tex">H_2=H_1-Dip</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mord mathdefault">i</span><span class="mord mathdefault">p</span></span></span></span>                 <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">H_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>相对于测者地平的视高度  <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>D</mi><mi>i</mi><mi>p</mi></mrow><annotation encoding="application/x-tex">Dip</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mord mathdefault">i</span><span class="mord mathdefault">p</span></span></span></span> 地平俯角</p>
<p>​						（参考地平基准从视地平变成测者地平）</p>
</li>
<li>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>3</mn></msub><mo>=</mo><msub><mi>H</mi><mn>2</mn></msub><mo>−</mo><mi>R</mi></mrow><annotation encoding="application/x-tex">H_3=H_2-R</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span></span></span></span>                    <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>3</mn></msub></mrow><annotation encoding="application/x-tex">H_3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>相对于测者地平的天体高度  <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>R</mi></mrow><annotation encoding="application/x-tex">R</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span></span></span></span> 蒙气差</p>
</li>
<li>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>4</mn></msub><mo>=</mo><mi>P</mi><mo>+</mo><msub><mi>H</mi><mn>3</mn></msub></mrow><annotation encoding="application/x-tex">H_4=P+H_3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>                    <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>4</mn></msub></mrow><annotation encoding="application/x-tex">H_4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>相对于天文地平的天体高度  <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span></span></span></span> 视差</p>
<p>​							（将参考地平基准从测者地平变成天文地平）</p>
</li>
<li>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>5</mn></msub><mo>=</mo><msub><mi>H</mi><mn>4</mn></msub><mo>±</mo><mi>S</mi><mi>D</mi></mrow><annotation encoding="application/x-tex">H_5=H_4\pm SD</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span></span></span></span>                 <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>5</mn></msub></mrow><annotation encoding="application/x-tex">H_5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>相对于天文地平的天体地心高度  <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>S</mi><mi>D</mi></mrow><annotation encoding="application/x-tex">SD</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span></span></span></span> 视半径</p>
</li>
</ul>
<h4 id="5-天体投影点的坐标">5、天体投影点的坐标</h4>
<h4 id="1-坐标">1、坐标</h4>
<p>1、天体投影点的坐标是在第一赤道坐标系（时角坐标系）下确定的。</p>
<ul>
<li>天体的格林时角GHA</li>
<li>天体的赤纬Dec</li>
</ul>
<h4 id="2-天体的格林时角gha">2、天体的格林时角GHA</h4>
<p>1、由于天体的周日视运动，恒星的格林时角GHA大约增加15°/h。</p>
<p>2、天体的春分点时角SHA：从春分点向西到天体时圈所夹的角距（顺时针）</p>
<p>​       SHA不随地球的旋转而改变（春分点是一个假想的不随地球自转的点）</p>
<p>3、天体的格林时角等于天体的春分点时角SHA和春分点的格林时角<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>G</mi><mi>H</mi><msub><mi>A</mi><mrow><mi>A</mi><mi>r</mi><mi>i</mi><mi>e</mi><mi>s</mi></mrow></msub></mrow><annotation encoding="application/x-tex">GHA_{Aries}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord mathdefault">G</span><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">A</span><span class="mord mathdefault mtight" style="margin-right:0.02778em;">r</span><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">s</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>之和：</p>
<img src="http://cos.pansis.site/202311222139737.png/abc123" alt="image-20231122213958666" style="zoom:50%;" />
<p>4、航海天文历提供的内容</p>
<ul>
<li>每小时的格林时角（GHA），针对春分点、太阳、月亮、4颗导航行星。</li>
<li>每隔3天的恒星的春分点的时角和赤纬。</li>
</ul>
<h2 id="三-航海高度差定位方法">三、航海高度差定位方法</h2>
<h4 id="1-相关概念">1、相关概念</h4>
<p>1、高度差法是航海天文定位的<strong>标准方法</strong>，使用方便。</p>
<p>2、时角</p>
<ul>
<li>地方时角LHA：起始经圈为测者午圈（地方午圈）。（自东向西，顺时针）(0h-24h或0°~360°)</li>
</ul>
<img src="http://cos.pansis.site/202311222206607.png/abc123" alt="image-20231122220635554" style="zoom:50%;" />
<p>经度Lon和时角的正向定义相反，Lon是东向为正，而时角是西向为正。</p>
<ul>
<li>子午圈时角t：与地方时角类似，范围是-180°-180°（西向为正，东向为负）</li>
</ul>
<h4 id="2-高度差法的基本原理">2、高度差法的基本原理</h4>
<ul>
<li>
<p>天体高度H是天体赤纬Dec、测者纬度Lat和子午圈时角t的函数，解天文三角形ΔZPσ得：</p>
<img src="http://cos.pansis.site/202311222230605.png/abc123" alt="image-20231122223026541" style="zoom:50%;" />
</li>
<li>
<p>在估计位置附近选一点作为假定位置AP(Lon, Lat)，利用上面公式计算获得天体的计算高度<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mi>c</mi></msub></mrow><annotation encoding="application/x-tex">H_c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> 。</p>
</li>
<li>
<p>高度差：由于假定位置AP和实际位置的差异所导致的<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mi>c</mi></msub></mrow><annotation encoding="application/x-tex">H_c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>和<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mi>o</mi></msub></mrow><annotation encoding="application/x-tex">H_o</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">o</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>之差，称为高度差。<img src="http://cos.pansis.site/202311222231259.png" alt="image-20231122223159213" style="zoom:50%;" /></p>
</li>
</ul>
<img src="http://cos.pansis.site/202311222232360.png/abc123" alt="image-20231122223219291" style="zoom:50%;" />
<ul>
<li>地方子午线和方位线AP-GP间的夹角，称为位置角<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>A</mi><mi>z</mi></msub></mrow><annotation encoding="application/x-tex">A_z</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.04398em;">z</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，其解算方法</li>
</ul>
<figure data-type="image" tabindex="1"><img src="http://cos.pansis.site/202311222232068.png/abc123" alt="image-20231122223256889" loading="lazy"></figure>
<ul>
<li>求天体的真方位角<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>A</mi><mrow><mi>z</mi><mi>N</mi></mrow></msub></mrow><annotation encoding="application/x-tex">A_{zN}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.04398em;">z</span><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，为从北点按照顺时针方向度量到天体方位圆。将 Az 修正到真方位角<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>A</mi><mrow><mi>z</mi><mi>N</mi></mrow></msub></mrow><annotation encoding="application/x-tex">A_{zN}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.04398em;">z</span><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> :</li>
</ul>
<img src="http://cos.pansis.site/202311222233647.png/abc123" alt="image-20231122223357588" style="zoom:50%;" />
<img src="http://cos.pansis.site/202311222234130.png/abc123" alt="image-20231122223408651" style="zoom:43%;" />
<h4 id="3-高度差法的具体步骤">3、高度差法的具体步骤</h4>
<img src="http://cos.pansis.site/202311222235963.png/abc123" alt="image-20231122223518891" style="zoom:53%;" />
<p><img src="http://cos.pansis.site/202311222235933.png/abc123" alt="image-20231122223537845" style="zoom:40%;" /><img src="http://cos.pansis.site/202311222235600.png/abc123" alt="image-20231122223552498" style="zoom:40%;" /></p>
<ul>
<li>需要注意的是高度差△H需要在纬度尺上量取。</li>
<li>高度差法的球面三角求解方法，忽略了真正等高圆的曲率，得到的位置值和真实的位置有几何误差。</li>
<li>当等高圆半径很大且AP点非常接近真实船位时，几何误差可以接受。</li>
<li>高度差法固有的几何误差可通过迭代法减小。</li>
</ul>
<h4 id="4-例题">4、例题</h4>
<img src="http://cos.pansis.site/202311222237717.png/abc123" alt="image-20231122223715636" style="zoom:53%;" />
<img src="http://cos.pansis.site/202311222237708.png/abc123" alt="image-20231122223729648" style="zoom:50%;" />
<h4 id="5-航行中的测定">5、航行中的测定</h4>
<p>航行中的舰船，需要考虑观测位置不同，与两次观测的时间差。</p>
<ul>
<li>根据前后两次观测时刻T1和T2，以及船速v，求得航行距离d = (T2 - T1 ) v，并且由罗经和陀螺罗盘测得船的航向C</li>
<li>利用前移位置线获得T2时刻的船位: 根据在T1时刻观测的结果得到位置线LOP1，任取Q点，根据航距和航向做有向线段QQ′，再做LOP1的平行线，即为前移位置线。</li>
</ul>
<figure data-type="image" tabindex="2"><img src="http://cos.pansis.site/202311222248393.png/abc123" alt="image-20231122224853285" loading="lazy"></figure>
<ul>
<li>当两次观测之间移动距离很远时，最好选择两个不同的且距各自的估计位置不太远的假定位置</li>
</ul>
<h2 id="四-航海其它天文定位方法">四、航海其它天文定位方法</h2>
<h4 id="1-观测北极星高度定纬度">1、观测北极星高度定纬度</h4>
<ul>
<li>测者在北半球，则天北极$ P_N $高度等于测者纬度。</li>
<li>北极星非常接近天北极（相距不到1°），其观测高度 需加上三项小的改正值，即可得到 <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>P</mi><mi>N</mi></msub></mrow><annotation encoding="application/x-tex">P_N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> 的高度，即测者纬度。</li>
</ul>
<img src="http://cos.pansis.site/202311222252983.png/abc123" alt="image-20231122225224901" style="zoom:50%;" />
<ul>
<li>
<p>计算公式</p>
<img src="http://cos.pansis.site/202311222253884.png/abc123" alt="image-20231122225315824" style="zoom:53%;" />
</li>
</ul>
<h4 id="2-观测天体中天高度确定纬度">2、观测天体中天高度确定纬度</h4>
<p><img src="http://cos.pansis.site/202311222335699.png/abc123" alt="image-20231122233556649" style="zoom:50%;" /><img src="http://cos.pansis.site/202311222335087.png/abc123" alt="image-20231122233535028" style="zoom:50%;" /></p>
<h4 id="3-利用太阳中天时刻定经度">3、利用太阳中天时刻定经度</h4>
<p>1、公式：<img src="http://cos.pansis.site/202311222350499.png" alt="image-20231122235002434" style="zoom:50%;" /></p>
<ul>
<li>
<p>上中天时， LAT显然等于12:00， <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>E</mi><mi>o</mi><msub><mi>T</mi><mrow><mi>N</mi><mi>o</mi><mi>o</mi><mi>n</mi></mrow></msub></mrow><annotation encoding="application/x-tex">EoT_{Noon}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord mathdefault" style="margin-right:0.05764em;">E</span><span class="mord mathdefault">o</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> 为算得的时差，则$ LMT = LAT –EoT_{Noon}$</p>
</li>
<li>
<p>GMT为太阳上中天时从天文钟读取值为<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>T</mi><mrow><mi>N</mi><mi>o</mi><mi>o</mi><mi>n</mi></mrow></msub></mrow><annotation encoding="application/x-tex">T_{Noon}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></p>
</li>
<li>
<p>《航海天文历》仅提供了每天GMT 0h和12h的时差EoT，还需根据该地太阳上中天世界时<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>T</mi><mrow><mi>N</mi><mi>o</mi><mi>o</mi><mi>n</mi></mrow></msub></mrow><annotation encoding="application/x-tex">T_{Noon}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>做内插处理求得<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>E</mi><mi>o</mi><msub><mi>T</mi><mrow><mi>N</mi><mi>o</mi><mi>o</mi><mi>n</mi></mrow></msub></mrow><annotation encoding="application/x-tex">EoT_{Noon}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord mathdefault" style="margin-right:0.05764em;">E</span><span class="mord mathdefault">o</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></p>
</li>
</ul>
<h4 id="4-利用2个天体的观测高度定纬度">4、利用2个天体的观测高度定纬度</h4>
<img src="http://cos.pansis.site/202311222354105.png/abc123" alt="image-20231122235441034" style="zoom:50%;" />
<p>已知量：天体<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>G</mi><msub><mi>P</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">GP_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord mathdefault">G</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>的<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>1</mn></msub><mi mathvariant="normal">、</mi><mi>D</mi><mi>e</mi><msub><mi>c</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">H_1、Dec_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord cjk_fallback">、</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mord mathdefault">e</span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，天体<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>G</mi><msub><mi>P</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">GP_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord mathdefault">G</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>的<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>2</mn></msub><mi mathvariant="normal">、</mi><mi>D</mi><mi>e</mi><msub><mi>c</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">H_2、Dec_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord cjk_fallback">、</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mord mathdefault">e</span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></p>
<p>计算的三角形：<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>△</mo><mi>O</mi><mi>G</mi><msub><mi>P</mi><mn>1</mn></msub><mi>G</mi><msub><mi>P</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\bigtriangleup OGP_1GP_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord">△</span><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault">G</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathdefault">G</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>   <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>△</mo><msub><mi>P</mi><mi>N</mi></msub><mi>G</mi><msub><mi>P</mi><mn>1</mn></msub><mi>G</mi><msub><mi>P</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\bigtriangleup P_NGP_1GP_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord">△</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathdefault">G</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathdefault">G</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></p>
<p>计算公式：</p>
<p><img src="http://cos.pansis.site/202311222359212.png/abc123" alt="image-20231122235937143" style="zoom:40%;" /><img src="http://cos.pansis.site/202311222359487.png/abc123" alt="image-20231122235951423" style="zoom:40%;" /></p>
<h2 id="五-航天纯几何天文导航">五、航天纯几何天文导航</h2>
<h4 id="1-基本原理">1、基本原理</h4>
<ul>
<li>通过测量<strong>一颗恒星</strong>和<strong>一颗近天体的夹角</strong>确定<strong>一个圆锥位置面</strong></li>
<li>再换另一颗恒星，测量其与同一近天体的夹角得到<strong>另一圆锥位置面</strong>；</li>
<li>两个圆锥面的交线即为航天器到近天体的位置线。</li>
</ul>
<img src="http://cos.pansis.site/202311250940060.png/abc123" alt="image-20231125093938536" style="zoom:50%;" />
<h4 id="2-基于2个近天体和3颗恒星观测几何解析定位法">2、基于2个近天体和3颗恒星观测几何解析定位法</h4>
<p>近天体到恒星的单位方向矢量 $\overrightarrow{s}  $ 已知，求近天体到航天器的单位方向矢量 $\overrightarrow{L}  $</p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault">A</span></span></span></span>为航天器测量出的近天体、航天器、恒星之间的夹角</p>
<img src="http://cos.pansis.site/202311250944514.png/abc123" alt="image-20231125094420457" style="zoom:100%;" />
<img src="http://cos.pansis.site/202311250945973.png/abc123" alt="image-20231125094543900" style="zoom:40%;" />
<p>利用2个近天体和3颗恒星即可观测到两条位置线$\overrightarrow{L_1} \overrightarrow{L_2} $ ，进一步解算航天器坐标</p>
<img src="http://cos.pansis.site/202311250948362.png/abc123" alt="image-20231125094827270" style="zoom:35%;" />
<p>最小二乘法求解</p>
<ul>
<li>
<p>特殊矩阵的便捷求逆</p>
<img src="http://cos.pansis.site/202311250950990.png/abc123" alt="image-20231125095059911" style="zoom:30%;" />
</li>
<li>
<p>最小二乘法求解结果</p>
</li>
</ul>
<img src="http://cos.pansis.site/202311250952357.png/abc123" alt="image-20231125095220297" style="zoom:37%;" />
<h4 id="3-两个近天体观察多于3颗恒星">3、两个近天体，观察多于3颗恒星</h4>
<p>即观测到位置线$\overrightarrow{L} $多于两条 ，进一步解算航天器坐标</p>
<img src="http://cos.pansis.site/202311250954683.png/abc123" alt="image-20231125095457605" style="zoom:30%;" />
<p>前提条件：在3次或N次测量的完成时间内，探测器和近天体没有相对运动。</p>
<h4 id="4-一个近天体和3个及以上的恒星">4、一个近天体和3个及以上的恒星</h4>
<p>利用一个近天体和3个及以上的恒星利用圆柱面确定位置线$\overrightarrow{L} $</p>
<img src="http://cos.pansis.site/202311250957841.png/abc123" alt="image-20231125095735787" style="zoom:30%;" />
<p>计算航天器到行星的距离r</p>
<img src="http://cos.pansis.site/202311251000099.png/abc123" alt="image-20231125100010033" style="zoom:40%;" />
<p>航天器相对于行星的位置矢量 <span class='katex-error' title='ParseError: KaTeX parse error: Undefined control sequence: \cal at position 32: …\ \ \ \ \left.{\̲c̲a̲l̲ ̲L}_{y}\ \ \ \ {…'>\vec{r}=r[ L_{x}\ \ \ \ \left.{\cal L}_{y}\ \ \ \ {\cal L}_{z}\right]^{T}</span></p>
<p>1、舰船天文导航的基本流程<br>
2、六分仪测角公式<br>
3、六分仪五个测量误差及公式<br>
4、水平视差HP定义、视差P公式<br>
5、需要改正视差的天体<br>
6、需要视半径修正的天体<br>
7、月亮水平视差HP和视半径SD之间的关系<br>
8、天体的格林时角计算公式<br>
9、地方时角LHA计算公式（和经度、GHA）<br>
10、子午圈时角的范围<br>
11、天文三角形计算H_c<br>
12、高度差法的具体步骤<br>
13、已知预估AP和两颗星的高度差和高度差，求真实AP（如果考虑航行中的因素）<br>
14、利用太阳中天时刻定经度的公式<br>
15、利用2个天体的观测高度定纬度流程<br>
16、航天纯几何天文导航基本原理<br>
17、基于2个近天体和3颗恒星观测几何解析定位法公式<br>
18、两个近天体，观察多于3颗恒星公式<br>
19、一个近天体和3个及以上的恒星</p>
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